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Sets and operations

Membership, subsets, union, intersection, complement, and Venn diagrams.

A set is a collection; the operations combine them: union (either), intersection (both), difference, complement. Picture it: a Venn diagram; each region is a combination of memberships. Think it: the operations satisfy the same laws as and/or/not, sets and logic are the same algebra (Boolean algebra).

हल किया गया उदाहरण · {1,2,3,4} union {3,4,5,6}

Set-Theory · Sets

{1,2,3,4} union {3,4,5,6}

चरण दर चरण

  1. A = \left\{1, 2, 3, 4\right\},\quad B = \left\{3, 4, 5, 6\right\}

    The two sets.

  2. A \cup B = \left\{1, 2, 3, 4, 5, 6\right\}

    Keep everything in either set.

  3. |A| = 4,\ |B| = 4,\ |A \cup B| = 6

    Cardinalities. Note |A ∪ B| = |A| + |B| − |A ∩ B|.

जवाब दिखाएँ
A \cup B = \left\{1, 2, 3, 4, 5, 6\right\}

अब आप कोई प्रश्न चुनें, या अपना प्रश्न टाइप करें या बनाएं। हर चरण, एक चित्र, और उत्तर तब तक छिपा रहता है जब तक आप न पूछें।

अपना काम सहेजकर रखें

एक स्वतंत्र वृत्तान्त प्रत्येक पाठ पर आगे कहता है, जो आपने पूरा किया है, आपके हल किये गये समस्याओं का रिकॉर्ड, और एक शिक्षक जिसके बारे में आप पूछ सकते हैं ।

साइन अप करें लॉगिन

यहाँ उपयोग में संकेत

पूरी परिभाषा, चित्र, और इसमें हर अक्षर का अर्थ क्या है?

कैसे: Sets and operations

  1. Write each set explicitly, or describe it by a property.
  2. For a union keep everything in either; for an intersection only what is in both.
  3. Check |A ∪ B| = |A| + |B| − |A ∩ B|.

लोग जो सवाल पूछते हैं

Are some infinities bigger than others?

Yes. The integers and the rationals can be listed; the real numbers cannot (Cantor's diagonal argument), so there are strictly more reals than integers.

What is the difference between a relation and a function?

A relation pairs inputs with outputs freely; a function is a relation in which every input gets exactly one output.

More in Set Theory & Logic

Relations, functions and equivalenceCardinality and infinityLogic and methods of proof